SDF - Solar-Aware Distributed Flow in Wireless
Sensor Networks
Immanuel Schweizer, Nils Fleischhacker, Dirk Bradler, Max Mühlhäuser and Thorsten Strufe
Technische Universität Darmstadt
Hochschulstrasse 10
64289 Darmstadt
Abstract—Energy is the most limiting factor in wireless sensor
networks. Harvesting solar energy is a feasible solution to
overcome the energy-constraint in some applications. It enables
a theoretically infinite network lifetime, sustaining a mode of
operation termed energy neutral consumption rate The challenge
arises, how can the harvested energy be utilized to maximize the
performance of the sensor network.
Considering a field monitoring application the performance
is measured as the sustained sampling rate of the sensors.
Maximizing the sampling rate needs to take the spatio-temporal
distribution of load and energy into account, to prevent the
overloading of nodes. In [1] they introduced a optimal, theoretical
solution based on perfect global knowledge.
In this paper we propose the solar-aware distributed flow (SDF)
approach. SDF enables each node to predict the harvested energy,
calculate a sustainable flow and control its local neighborhood.
To the best of our knowledge it is the first practical solution.
Extensive simulations confirmed that SDF achieves over 80% of
the theoretical optimum, while introducing negligible overhead.
I. I NTRODUCTION
Harvesting environmental energy has become a valid approach to overcome the hard limit imposed by battery capacity,
either by supplementing or replacing the battery [2], [3], [4],
[5], [6]. Harvested energy is potentially infinite. This reflects
a paradigm change to the field, since it enables an entirely
new mode of operation. The lifetime of sensor nodes, under
absence of hardware failures, suddenly can be considered to
be infinite. The nodes in this mode are termed to operate at
an energy neutral consumption rate.
The main challenge for a traditional sensor network is
to maximize the lifetime of the nodes, while guaranteeing
a certain network performance, e.g., delay, sampling rate,
or tracking accuracy. Considering the possibility to harvest
energy, the challenges of ultra-low power operations remain
similar, yet, two new challenges emerge: Can the energy
neutral operation be guaranteed for each node in the network
sustaining the aforementioned network performance. And can
the network performance be maximized while still guaranteeing energy neutrality. Since the performance of the network
and the energy neutral consumption rate depend on the spatiotemporal distribution of both energy and load throughout the
network, these are non-trivial challenges.
Considering a field monitor application, increasing the
sampling rate of the sensor nodes represents the inertial
requirement. In field monitoring sensors observe a phenomena
sending periodic data messages to a basestation. By increasing the sampling rate the granularity of the observation is
increased. This comes at the cost of additional load to the
network and increased energy consumption at each node.
In this paper we tackle the problem of how to maximizing
the sampling rate in a solar-powered field monitoring application.
This problem was first introduced by Kansal et al. [1]. They
established a theoretical solution for the homogeneous case.
In the homogeneous case all nodes are assumed to sample at
the same rate. We will assume heterogeneous sampling rates
are possible. Their solution is to solve linear equations based
on global knowledge. Obtaining this global knowledge about
energy production, energy levels and the overall topology is
not feasible. But their solution gives a theoretical optimum.
The problem of maximizing the sampling rates consists of
two subproblems. Most importantly the sampling rates have
to be maximized. Here the energy harvested must be taken
into account. But also the possible communication throughput
of any node in the network, as this might impose a limit on
the data that can be transmitted energy neutral. The second
problem is more general. The flow has to be routed from the
nodes to the basestation. Throughout this paper we will assume
a given routing algorithm.
In this paper we will introduce the solar-aware distributed
flow (SDF) approach. To the best of our knowledge it gives the
first practical solution to the problem of maximizing sampling
rates for field monitoring.
SDF acts in the three steps of (a) establishing an estimation
of the long term energy production, (b) calculating the maximum communication flow the node will be able to handle,
and (c) distributing the possible flow to the direct neighbors.
Evaluating solar-aware algorithms poses the additional challenge of modeling environmental condition, i.e., solar radiation
levels. Clouds or other objects might obstruct the sunlight. This
can be mitigated by using real world solar radiation data that
must be obtained before [1]. Accurate, detailed cloud models,
as found in meteorology [7], [8], are highly complex. Yet,
to cover worst case scenarios for a solar-aware flow control,
we introduce a simpler model. Covering moving shades,
overlapping and fluctuating cloud density, are sufficient.
Our main contribution is SDF, the first practical approach
to sampling rate maximization in field monitoring. Extensive
simulations of SDF show that it achieves a minimum sampling
rate of 80% of the theoretical optimum.
The paper is organized as follows. Section II outlines the
related work. Section III will introduce the basic models
and assumptions. SDF will be introduced in Section IV. In
Section V some basic properties of SDF are discussed. The
results of the evaluation will be presented in Section VI.
Finally Section VII will conclude the paper and give a short
outlook.
II. R ELATED W ORK
The feasibility of energy harvesting wireless sensor networks has been studied extensively in the recent past. Roundy
et al. [9] review a great variety of potential power sources
for wireless sensor networks. While they review the classical
power storage in batteries and even micro fuel cells or micro
heat engines they also research the potential of different
energy harvesting techniques. These techniques include photovoltaics (i.e. solar panels), temperature gradients, human
power, wind/air flow and vibrations. They showed that solar
panels offer the highest power density. If the sensor network is
deployed such that solar panels can be used this makes them
the best choice for reliably powering sensor nodes.
Figure 1.
A solar harvesting sensor node (Heliomote [2])
Another advantage of solar energy is that it is uncontrolled
but predictable [1]. Predicting the availability of harvested
energy is the basis of any harvesting sensor network. The
prediction is used to adapt the duty cycle during times with
no or insufficient energy [10] or to assign task to nodes with
more energy [11].
Several working prototypes of wireless sensor nodes using
solar power have been developed, showing that solar powered
wireless sensor networks are indeed feasible. Raghunathan et
al. [2] present the Heliomote (cmp. Fig. 1) – a Mica2 [12] mote
enhanced with a circuit board equipped with a solar panel and
NiMH batteries for solar energy harvesting. They show that in
principle their device is capable of near perpetual operation.
Jiang et al. [3] design and implement Prometheus – a
wireless sensor node based on the Telos-mote [13] with a solar
panel, super-capacitors and Li-ion batteries. They present and
discuss results from a ten day period.
Minmi et al. [4] present Solar Biscuit, a wireless sensor
node without a battery, solely relying on a solar panel and a
super-capacitor, for environmental monitoring.
Sikka et al. [5] present Fleck1 a solar powered wireless
sensor node using a solar panel and NiMH batteries. Their
main contribution is the incorporation of a DC-DC converter
enabling deeper battery discharge cycles between periods
where solar power is available. In [14] they present results
of a network operating 24x7 for over two years.
Alippi et al. [6] develop and present a wireless sensor
network framework based on solar powered sensor nodes. The
wireless sensor network is deployed in Moreton Bay, Brisbane,
Australia to deliver temperature and luminosity data of the
marine ecosystem. They present and discuss results from a
four day period.
To make the operation of environmentally powered wireless
sensor networks more efficient, several solar-aware protocols
have been developed. Some focus on solar powered wireless
sensor networks while others use a more general approach.
Lin et al. [15] developed E-WME (Energy-opportunistic
Weighted Minimum Energy) an energy-aware routing algorithm for wireless sensor networks. It works with any environmental energy sources and they show that their routing
scheme is asymptotically optimal. Other solar-aware routing
approaches based on directed diffusion [16] can be found
in [17], [18], [19].
Voigt et al. [20] present a solar-aware clustering protocols
that is based on a centralized and distributed variant of
LEACH [21]. Their simulation results suggest a significant
increases in lifetime from the solar-aware protocols compared
with their not solar-aware counterparts. All of the approaches
only try to handle a given load better. None is really looking
at how the network load can be increased by utilizing the
harvested power.
Some related work exists on the topic of assigning sampling
rates in wireless sensor networks. Shu et al. [22] try to
optimize the network sampling rates in terms of a scheduling
problem. They try to maximize network throughput without
taking energy consumption into consideration.
Bandyopadhyay et al. [23] analyze what tradeoffs in sensor
density, energy usage, throughput and delay have to be made
to achieve certain temporal and spatial sampling rates. But
those sampling rates are always fixed and predefined.
The problem of maximizing sampling rates in solar harvesting sensor networks is first discussed by Kansal et al. in [1].
They describe a field monitoring application with the goal
to maximize homogeneous sampling rates while remaining
energy neutral. There approach is to model the flow in the
network by using linear equations. Solving the linear equations
yields one sampling rate and a corresponding flow that can be
sustained by all nodes using no more than the energy neutral
consumption rate. To calculate the solution global knowledge
is needed over all nodes, flows and energy in the network.
This is not feasible for a real-world sensor network.
What is missing is a distributed approach to maximizing
sampling rates. If we take harvested energy into account we
are no longer dealing with predefined sampling rates. It no
longer suffices to optimize the nodes to sample at a given
rate and deliver a given flow. We need to predict the available
energy to utilize it as much as possible. And while they state
the problem in [1] they fail to give a real-world solution. To
the best of our knowledge there is no practical solution to the
(a) The network graph G
Figure 2.
(b) Valid routing graph for b
(c) Invalid routing graph since n has two active
routes to b
Examples of valid and invalid routing graphs derived from the same network graph
problem yet.
III. P RELIMINARIES
The following section defines preliminaries and the models
used for SDF and throughout this paper.
SDF will abstract from any given routing algorithm. The
corresponding routing graphs needs to adhere to some basic
properties we are going to outline here.
We introduce an energy model for nodes supplemented with
a solar panel. Battery, solar panel and energy drains are defined
here. A model for the solar radiation depending on time of
year, time of day and geographical latitude is established. It
gives a basic solar radiation level. To account for variations
in the spatio-temporal distribution of the solar radiation we
define a cloud obstruction model.
A. Routing Graph
SDF is targeted at field monitoring. We will assume a single
base station b to serve as data sink. The network can be
abstractly modeled using a directed graph G = (N, E) with
N being a set of vertices representing the network nodes and
E being a set of edges with (v1 , v2 ) ∈ E if and only if v1 can
send directly to v2 .
We designate as routing graph of node x or RG(x) =
(N, R) the subgraph of the network graph G = (N, E) for
which
R = {r|r ∈ E ∧ ∃v (v ∈ N ∧ r ∈ path (v, x))} .
Figure 2(a) shows an example network graph G. While
2(b) shows a routing graph that is valid, 2(c) shows a routing
graph that would be invalid under this assumption. For node n
in figure 2(b) there is only one active path from n to b, while
in figure 2(c) there are two. Different routing algorithms have
been proposed that fulfill this requirement and we refer to the
respective publications [24].
Stability:
The nodes are assumed to be stationary. The topology might
still change due to weak mobility, e.g., failure of nodes or
changes of connectivity. SDF is able to compensate this by
periodic update propagation.
(a) Due to link failure (dashed
line) a internal node is now a
leaf node
Figure 3.
(b) Due to the left node failing a
leaf node is now a internal node
Worst cases due to weak mobility
Thus RG(b) is the graph consisting of all paths that are
used to route a packet from any node to the base station.
The layout and the properties of RG(b) depend heavily on
the used routing algorithm. Therefore we need to discuss the
following two assumptions made about RG(s).
In worst case a internal node becomes a leaf node or vice
versa (cmp. Fig. 3). We will see how SDF deals with those
cases during the discussion later.
Simplicity and Connectivity: It is assumed that from
any node n in RG(b), there exists exactly one active path
to b. The resulting RG(b) is a directed tree. For any node n
we can define s as the direct successor and P as the set of
predecessors in the routing graph.
The energy model reflects three basic parts. A battery for
energy storage, a solar panel to harvest energy and recharge
the battery and a set of energy drains, modeling the energy
consumption of the node’s hardware such as CPU, radio and
sensors.
B. Energy Model
A new energy level for time ti+1 can be calculated as
E (ti+1 ) = min(Cmax , E (ti ) + H (ti , ti+1 ) − D (ti , ti+1 ))
where E(t) is the Energy stored at time t, H(ti , ti+1 ) is the
energy harvested by the solar panel, D(ti , ti+1 ) is the amount
of energy consumed by the energy drain D and Cmax is the
maximum battery capacity. The energy neutral consumption
rate pn is reached if H (ti , ti+1 ) = D (ti , ti+1 )).
Battery: The battery is assumed to be an ideal storage
for electric energy. The battery has a fixed capacity Cmax
up to which it can be charged. For the sake of simplicity we
assume that it does not have internal leakage currents and
does not age or develop a memory effect due to recharging.
We assume it to be completely insensitive to all environmental
conditions. Cmax has to be high enough to sustain the node
for at least one day on full load. With sensor platforms
allowing nodes a lifetime of several months on a single
battery this assumption is easily valid.
Solar panel: The solar panel offers two basic functionalities.
It is possible to determine the current power output and
the energy accumulated over a specified time interval. The
energy harvested between ti and ti+1 can be calculated as
H (ti , ti+1 ) = r (ti , ti+1 ) · A · e where A is the panel area, e is
a fixed efficiency constant and r is the solar radiation inbound
to the node’s location. Again for the sake of simplicity we
assume a fixed efficiency. While it might change over time
due to, e.g., the panel’s orientation towards the sun, this does
not effect the prediction of the inbound solar energy. The
model for solar radiation will be introduced later.
Energy Drains: Energy drains model how much energy
different hardware parts have consumed between ti and ti+1 .
We use a discrete event model for the different energy drains.
Each event, e.g, the change of the CPU’s duty cycle, triggers
a recalculation of the remaining energy.
The CPU’s energy consumption is modeled by active drain
a, idle drain i and a duty cycle rate r. It is calculated as
Dc (ti , ti+1 ) = (ti+1 − ti ) · (r · a + (1 − r) · i) .
The radio’s energy consumption is modeled by the radio’s
state s and fixed drain d(s) for each state. The states are
receive, transmit, on and sleep. If sc is the radio’s current
state, the drain is calculated as
Dr (ti , ti+1 ) = (ti+1 − ti ) · d(sc ).
The sensor’s energy consumption is modeled similarly. A
sensor has an active state a and an idle state i. If sc is the
current state of the sensor, the drain is calculated as
Ds (ti , ti+1 ) = (ti+1 − ti ) · d(sc ).
The total energy drain is
D(ti , ti+1 ) = Dc (ti , ti+1 ) + Dr (ti , ti+1 ) + Ds (ti , ti+1 ).
The next step is to model the environmental conditions that
influence the solar radiation and therefore the harvested power
at each node.
C. Solar Radiation Model
The solar radiation model is based on Brock [25], altered
to yield a higher granularity.
The solar radiation R for a given point P and time t is
calculated as
s
· cos (α(P, t))
R(P, t) = max 0,
v(t)2
Here s is the solar constant (s = 1353W m−2 [25]), v is the
radius vector and α is the zenith angle.
The radius vector is used to correct the ellipticity of the
earth’s orbit. The zenith angle is the angle between the
zenith and the position of the sun. It is calculated using the
declination d(t) and minute angle β(t). The declination is the
angular difference between the equator and the position of the
sun at solar noon. The declination can be calculated approximately using the obliquity of the ecliptic as specified by the
international earth rotation & reference systems service [26].
The minute angle is the angle between the sun and the south
point for a certain minute of the day. As the earth moves
π
720 per minute, the minute angle can be calculated as β =
π
(m − 720) · 720
, where m is the minute of the day i.e. the
number of minutes that have passed since midnight.
D. Cloud Obstruction Model
Solar-aware algorithms have to adapt to variations in the
spatio-temporal distribution of solar energy in outdoor environments. This is mainly due to static objects, i.e., buildings
or trees, or moving objects, i.e. clouds, covering sensor nodes.
The prediction of solar energy should be able to adapt to
changing energy levels due to obstruction. This is easy for
static objects since they obstruct roughly the same amount of
solar energy every day. Moving objects like clouds are much
harder to predict. In this respect clouds are a worst case for
solar energy prediction. They are moving, overlapping, and
the cloud density changes over time.
In [1] they model the spatio-temporal distribution of solar
radiation by using real world data that is captured a priori. This
introduces the overhead of capturing such images and might
only cover the solar profile of a specific region. Detailed cloud
models as used in meteorology [7], [8] are far too detailed and
complex.
We will introduce a simple cloud model to cover the worst
cases for SDF. We will assume a given mean cloud density.
A variance is introduced that accounts for possible changes
in cloudiness. The mean and variance are input parameters
of the model. The probability of a given cloudiness decreases
when moving away from the mean. This is intuitively covered
by assuming a normal distribution for the cloud density with
a fixed mean µ and variance σ, where µ ≥ 0. Thus the
probability density is given by:
1 x−µ 2
1
φ (x) = √
· e− 2 ( σ )
2·π
The model works in discrete time steps and a new density
is calculated dependent on the normal distribution. Clouds are
either removed or added until the new density is reached. The
clouds themselves are modeled as randomly placed ellipses
with the properties of transparency, speed, and direction. Since
some clouds obstruct more radiation and clouds might overlap
we need the notion of transparency t. The minimal and
maximal transparency tmin , tmax ∈ [0, 1] can be set as input
parameter.
The total solar radiation after obstruction S at point P and
time t can thus be calculated as
Y
S(P, t) = R(P, t) ·
t(C).
C∈clouds
P ∈C
This model offers a simple way to evaluate a solar-aware
algorithm under worst case conditions.
IV. S OLAR -AWARE D ISTRIBUTED F LOW
Solar-aware distributed flow (SDF) wants to maximize the
sampling rates achieved by each node while allowing energy
neutral operation. The basic idea is that energy is mainly
consumed due to either generating flow or relaying flow. Since
each node has to forward the messages of all predecessors P in
the routing graph it will issue control messages to the direct
predecessors granting them allowed flow. So from a node’s
perspective SDF consist of three main steps that are repeated.
• Predict the consumption rate c
• Calculate the own sampling rate and the allowed flow of
the predecessors P
• Send control messages to all direct predecessors in P and
set the own sampling rate
Algorithm 1 S OLAR - AWARE DISTRIBUTED FLOW
Input: Allowed flow fa from successor
Output: Sampling rate x and allowed flow fa to direct
predecessors
c ← C ONSUMABLE -P OWER
x ← C ALCULATE -F LOW
D ← G ET-D IRECT-P REDECESSOR -S ET(P )
for all p ∈ D do
Pp ← G ET-F ORWARDED(P, p)
S END -F LOW-U PDATE -M ESSAGE(pred , x ·S IZE(Pp ))
end for
S ET-S AMPLING -R ATE(max(xmin , x ·s))
Algorithm 1 gives a sketch of one round of SDF. This will
be repeated periodically on each node to yield a maximized
sampling rate utilizing as much harvested energy as possible.
A. Consumable power
The first step is to predict the harvested energy. Since solar
energy is classified as uncontrolled but predictable [1] this
is indeed possible and different methods have already been
proposed [1], [11], [10]. They are usually implemented to duty
cycle nodes to use less or no energy if less or no energy is
harvested. We want to minimize the fluctuation of the sampling
rate, e.g., over night. Therefore we need a simple conservative
method that approximates the energy neutral consumption rate
over a longer time span. Generally speaking the energy neutral
consumption rate pn between ti and ti+1 is defined such that
the battery level E(ti ) = E(ti+1 ). If the function H(t) models
the harvested power over time we can also state that
Z ti+1
H(t) dt
ti
.
pn =
ti+1 − ti
We will define the predicted consumption rate c and it
should be bound by c ≤ pn .
We do not know H(t) for the future. But we can approximately sample the energy neutral consumption rate for the
past. Recall that in our model the solar panel can return the
energy accumulated over a specified time interval. This might
not be feasible with all implementations. In this case one can
reside to measuring battery levels. This is less accurate but
might be suffice if the difference between ti and ti+1 is large
enough.
We take several such samples at fixed time intervals. We
then use their distribution to calculate c. We assume the
samples S follow a normal distribution N µ, σ 2 , where
P
P
(s − µ)2
s
s∈
S
s∈ S
and σ 2 =
.
µ=
|S|
|S|
We will then take a quantile of this distribution. The x%
quantile is defined such that at most x% of the assumed
distribution may lie below that value. For our approach we will
take the 10% quantile as a very conservative approximation of
c. If we assume a fixed energy neutral consumption rate pn the
mean of the distribution will converge against pn . By using
the 10% quantile we introduce a buffer. This will allow the
model to handle inaccurate measurements and gives time to
adapt to changes in the incoming solar energy.
Figure 4 gives an example as how this is applied to real
samples. If the variance is reduced the quantile yields higher
values.
At the beginning samples might be highly scattered. Assume that the network starts operation at 9am and the first
sample is taken at 4pm. This will yield a high energy neutral
consumption rate as the node was able to harvest energy all
the time. Similarly if we start at night the first sample might
yield 0. Since the approximation is getting better over time
we add an initialization period of 24 hours where no samples
are taken. This will prevent extreme outliers at the beginning
to distort the calculations. After that samples will be taken at
an interval of 7 hours.
To calculate a meaningful distribution a sufficient number
of samples have to be retained. We will evaluate how much
samples are sufficient later. To account for this, we will scale
down c even further, until we reach a sufficient number of
samples. We introduce an additional factor called sample
confidence sc. sc is 0 if the number of samples is below two,
0.35
250
probability density
0.3
probability density
assumed distribution
samples
0.25
0.2
0.15
0.1
0.05
0
150
100
50
0
-2
0
2
4
6
8
10
4.3 4.32 4.34 4.36 4.38 4.4 4.42 4.44 4.46
energy neutral consumption
rate in mW
(a) Samples with higher variance
Figure 4.
quantile.
assumed distribution
samples
200
energy neutral consumption
rate in mW
(b) Samples with lower variance
The samples of the energy neutral consumption rate and the distributions assumed from them. The dotted line shows the distributions’ 10%
1 if the number of samples is sufficient and scales linear in
between.
We return c = sc ∗ c as the predicted consumption rate. It
is simple to calculate, while giving a good approximation and
leaving buffer for sudden changes in solar radiation.
B. Calculate flow
If c is known, the node can calculate the sampling rate for
itself, and the allowed flow for the predecessors. The first step
is to determine the routing graph predecessors.
If a message is sent from node n to the basestation b it
contains both n and b. Let x be a node on the path from
n to b and p be the direct predecessor of x on that path. x
can now store that n is a predecessor that is routed through p.
Following this procedure each node can save a map containing
all predecessors and the corresponding direct predecessor.
Figure 5 gives an example of how the resulting map looks like.
Since this map might change due to weak mobility each entry
is timestamped. Since we have a periodic flow of messages
updates propagate quickly.
Any amount of flow x the node chooses to use for its own
samples requires x · (Psense + Ptx ). Any amount it allocates
to any predecessor requires x · (Prx + Ptx ). Here Psense , Ptx
and Prx are the power needed to sense, transmit or receive a
given data rate r respectively. They are given by the hardware,
e.g. for the CC2420 radio used in the MicaZ [27] mote Prx =
62mW and Ptx = 57.42mW (0dBm) [28] at a data rate r =
250kbps.
So basically each node with |P | = n has to solve
!
n−1
X
xi · (Prx + Ptx ) + xn · (Psense + Ptx ) = c
i=0
and allocating flow xi to predecessor pi for i ∈ {0, . . . , n − 1}
and flow xn to itself. In SDF each predecessors is treated
equally leading to
n · x · (Prx + Ptx ) + x · (Psense + Ptx ) = c.
Solving this for the flow x leads to
x=
5
3
c
.
n · (Prx + Ptx ) + (Psense + Ptx )
4
1
2
n
s
1 {1}
2 {2,3,4,5}
(a) A example (b) The predecessor map
routing graph
of node n
Figure 5. An example of the predecessor map of node n in a network of
seven nodes
We can now easily determine the direct predecessors and
the total number of predecessors |P |. There are essentially two
different things, that c may be utilized for. The node may either
choose to sense its environment, producing samples itself and
sending them to base station. Or it allows its predecessors to
increase the amount of data sent. Both choices use a certain
amount of energy.
But the flow is not only bound by the available power but
also by the successor. If fa denotes the allowed flow from the
successor (fa = ∞ if s = b) and (n + 1) ∗ x > fa we set
fa
x = n+1
.
As result x gives both the own sampling rate and the allowed
flow for each predecessor in P .
C. Control messages
Each node n sends regular control messages to the direct
predecessor that contain the allowed flow fa . For a predecessor
p fa = x ∗ |Pp | where Pp is the set of all predecessors routed
through p and p itself. n will set its own sampling rate to
max(xmin , x ∗ s). Here xmin is the minimum sampling rate
that is used during the initialization or if not enough energy
can be harvested to guarantee a minimal service level.
V. D ISCUSSION
This section will discuss the update propagation and performance implications of the SDF protocol. For the update
propagation we focus on worst case analysis. The performance
is shown to decrease with the hop distance to the basestation.
A. Update propagation
Each node starts with no allowed flow and is using the
minimum sampling rate. If a node is d hops away from the
basestation it will take d − 1 hops until it receives an update
issued by a node directly attached to the basestation. In the
worst case d might be n if n is the number of nodes. This
happens if all nodes are lined up, such that they are only
connected to one successor and predecessor. So in worst case
it takes n − 1 rounds until each node has received one update.
If the nodes are randomly placed on a quadratic field, what
we get on average is a control tree. Here updates propagate in
log n time.
Lets revisit the worst case example illustrated in Figure 3.
In the first case a internal node becomes a leaf node (cmp.
Fig. 3(a)). Now the possible sampling rate is much higher
since no energy is needed to relay messages. The predecessor
map is updated if no more messages are received. Therefore
it takes one round of SDF for the node to adjust it sampling
rate. One round where there was less energy consumed than
possible.
The second case is a leaf node that becomes an internal
node (cmp. Fig. 3(b)). In the worst case it was a leaf node l
directly attached to the base station and is now connecting all
remaining n − 1 nodes to the base station. Let us assume that
the allowed flow for the remaining nodes is much higher than
l can handle. l also uses all its power for sampling the sensors.
So l is using more energy than the energy neutral consumption
rate. Again it takes one round until n has knowledge of all
predecessor and can adjust the own sampling rate accordingly.
We have already established that in the worst case it now
takes n − 1 rounds for this update to propagate to all the
attached nodes. It takes a total of n rounds until the node
is again working with the energy neutral consumption rate.
But at each round another node will receive the message and
reduce its sampling rate. So the total power needed to relay
the messages will converge to the energy neutral consumption
rate. We take an update interval of 30 minutes for SDF. This
means an update can propagate 48 hops in 24 hours. We will
leave it to the reader to assess if a sensor network should
route messages over more than 48 hops. But with SDF we
only consider maximizing the sampling rate not optimizing the
routing graph, so it might indeed become a problem. Adjusting
the update interval accordingly to balance between update
propagation and control overhead.
B. Performance
Longer paths lead to a higher delay in update propagation.
But longer paths also lead to a lower minimal sampling
rate. The minimal sampling rate is the lowest sampling rate
achieved by any node during the operation of the network.
Let us assume a network where each node, that is more
than one hop away from the basestation, is not bound by
its consumption rate. It is instead bound by the allowed flow
granted by the successor. And let us also assume that there is
only one node n directly attached to the basestation. Then the
whole network will use the same sampling rate r, which is
bound by the consumption rate of n. Now consider the same
example but we now assume that there is one node ni 6= n that
is bound by the own consumption rate. ni will now calculate
a flow x < r. So ni and all predecessors of ni will have
a sampling rate ri ≤ x < r. From here on it is trivial to
proof that there exists a leaf node l with sampling rate rl
and rl ≤ r∀r ∈ R. R is the set of all sampling rates in the
network. The main idea of a proof is based on the fact that the
own sampling rate is either bound by the allowed flow of the
successor or by the own consumption rate in which case it is
either equal or lower than the sampling rate of the successor.
On a similar note it can be shown that there exists a node
n, directly connected to the basestation, with sampling rate rn
with rn ≥ r∀r ∈ R. Again the idea is that nodes are bound by
their successor or the consumption rate. Since nodes attached
to the base station are not bound by their successor, but all
their predecessors are bound by them, this result is obvious.
VI. E VALUATION
We evaluate our approach using the SIDnet-SWANS simulator [29]. SIDnet-SWANS is a fast event-based simulator for
wireless sensor network based on Jist-SWANS [30].
We will use the theoretic optimum introduced by Kansal et
al. [1] as the baseline. The baseline can only be calculated at
the end of the simulation when all the relevant information is
available. It calculates a multi path flow that can be sustained
with knowledge of the energy neutral consumption rate. This
represents the optimum, which is only possible to reach with
global knowledge and a very good performance benchmark
for SDF.
First we will describe the simulation setup. Then we will
look at the initialization and the performance of SDF. The last
step is to evaluate the overhead introduced by SDF.
A. Simulation setup
Unless otherwise noted the simulations are configured as
follows. Each simulation will run for 480 hours starting on
January 1st at 12:00 am. It is set at a latitude of 50◦ N with a
mean cloud density of 0.6 and a cloud density variance of
0.3. This will roughly correspond to the solar radiation in
Darmstadt, Germany. The effects of the cloud density will be
evaluated later.
There are 30 nodes randomly positioned on a square field
with a side length of 3, 500 feet. The solar panels have an
area of A = 9cm2 and an efficiency e = 0.2. They operate
with a minimum sampling rate of 2.96 bit
s . Samples for the
consumption rate are taken every 7 hours and 30 samples
are retained. The 10% quantile is chosen and the sample
confidence is set to 0.5.
We use the simple geographic greedy routing algorithm
implemented in SIDnet-SWANS. It is similar to GPRS [24],
without route recovery. Update messages are sent every 30
minutes.
Each configuration is run 20 times with different random
seeds.
B. Initialization Phase
During the initialization all nodes start off using the minimum sampling rate. As the number of samples increases the
consumption rate can be approximated better. We evaluate first
how much samples have to be retained.
ratio to neutral consumption rate
1.2
1
0.8
0.6
0.4
5 Samples
10 Samples
20 Samples
30 Samples
40 Samples
0.2
0
0
50
100
150
200 250 300
time in h
350
400
450
500
Figure 6. The ratio of the maximal calculated consumption rate to the energy
neutral consumption rate for different numbers of retained samples.
Figure 6 illustrates the impact of changing the number
of samples retained. We compare the calculated maximal
consumption rate to the energy neutral consumption rate. If we
retain too many samples the consumption rate will converge
slower. This makes it harder for a node to react to changes in
solar radiation. If we retain too few samples the consumable
power might get higher than the energy neutral consumption
rate. If we retain 30 samples we get a good balance between
convergence time and quality of approximation. We can also
note that after the transient phase is over, the predicition
SDF uses is well over 90% of the possible energy neutral
consumption rate. This indicates a good performance of the
prediction while leaving some buffer for sudden changes in
environmental conditions.
C. Performance Evaluation
The most important benchmark for SDF is the sustained
sampling rate. As noted before we will compare SDF to the
baseline in [1]. We already stated that the baseline assumes a
homogeneous sampling rates. This implies that the sampling
rate is bound by the weakest node in the network. We measure
the sampling rates for SDF and the baseline at the end of
the simulation time after 480 hours. For SDF we obtain the
minimal, maximal and average sampling rate achieved in the
network. For a fair comparison the minimal sampling rate is
evaluated against the baseline as it gives the performance of
the weakest node. We also show the average and maximal
sampling rates as they illustrate the advantage of allowing
heterogeneous sampling rate.
We keep the deployment area fixed. Thus by changing the
number of nodes we will change the node density. We do
abstract from the routing algorithm. But in general increasing
the node density will lead to longer average paths. As stated in
the discussion this implies a possible decrease in the minimal
sampling rate obtainable.
Indeed the aforementioned effect is exhibited in Figure 7(a).
Increasing the node density has almost no effect on the
baseline while the minimal sampling rate for SDF drops from
34bps to 30bps. The baseline performs better due to the
global knowledge on all possible connections between nodes.
Figure 7 presents the relative performance of the minimal,
average and maximal sampling rate to the baseline. SDF is
capable of sustaining over 80% of the baseline performance.
It is important to note that while the minimal sampling rate
drops the maximal sampling rate increases. Since we increase
the node density the number of nodes directly attached to the
basestation increases. Both effects, longer average path length
and more nodes directly attached to the basestation, lead to
the divergence between minimal and maximal sampling rate.
On average the sampling rate achieved by SDF stays almost
constant.
Increasing the cloud density leads to a drop in the average
consumption rate. Thus it must lead to a decrease in all sampling rates. As energy gets scarce the performance becomes
crucial. The baseline gives a theoretical optimum. SDF should
converge against the baseline as cloud density increases.
Figure 8 illustrates the variation in cloud density. In relation
to the baseline the sampling rates achieved with SDF are
slightly increasing (cmp. Fig.8(b)). With a mean cloud density
of 1.0 we achieve over 85% of the baseline performance for
the minimal sampling rate.
D. Control Message Overhead
SDF introduces control messages. Each node sends one
message to each direct predecessor per round. Leaf nodes send
no messages. If n is the total number of nodes in the network
and m the number of messages sent each round we note that
m < n.
The goal of SDF is to maximize the load in the network.
So introducing additional load is acceptable if it is small
compared to the performance gained. We evaluate both the
message and bit ratio to the total number of messages and bit
send. The bit ratio is important since compared to messages
containing sensor data, control messages are small.
The worst case for both ratios is the initialization phase.
Each node samples at the minimal sampling rate. The amount
of data is small. Since the control overhead is fixed this marks
the worst case.
Obviously the overall shape of the message and bit ratios
are similar (cmp. Fig. 9). We observe that during the 24 hours
of initialization nothing really happens. The message ratio is
around 35% with a peak of 43%. So even though all nodes
sense at the minimum sampling rate less than 50% are control
messages. We also observe the spikes every 30 minutes when
control messages are sent. For the bit ratio, even though the
40
average sampling rate
minimal sampling rate
maximal sampling rate
1.2
ratio to optimal sampling rate
38
sampling rate (bps)
36
34
32
30
28
0
10
20
1.1
1.05
1
0.95
0.9
0.85
minimal sampling rate
optimal sampling rate
26
1.15
0.8
30
40
50
number of nodes
60
70
80
0
10
20
30
40
50
number of nodes
60
70
80
(a) The minimal sampling rates achieved after 480 hours compared with (b) The ratios of the average, minimal and maximal sampling rates in
the optimal sampling rates
relation to the optimal sampling rate
Figure 7.
The impact of the node density on the average, minimal and maximal sampling rates
45
1.3
average sampling rate
minimal sampling rate
maximal sampling rate
ratio to optimal sampling rate
sampling rate (bps)
40
35
30
25
1.2
1.1
1
0.9
minimal sampling rate
optimal sampling rate
20
0.8
0
0.2
0.4
0.6
0.8
cloud density mean
1
1.2
0
0.2
0.4
0.6
cloud density mean
0.8
1
(a) The minimal sampling rate achieved after 480 hours compared with (b) The ratio of the average, minimal and maximal sampling rate in
the optimal sampling rate
relation to the optimal sampling rate
Figure 8.
The impact of the mean cloud density on the average, minimal and maximal sampling rates
0.45
0.035
0.03
0.35
control message overhead
control message overhead
0.4
0.3
0.25
0.2
0.15
0.1
0.025
0.02
0.015
0.01
0.005
0.05
overhead by messages
overhead by bits
0
0
0.1
1
10
time in h
100
1000
(a) The message overhead caused by the control messages
Figure 9.
0.1
1
10
time in h
100
1000
(b) The overhead in bit caused by the control messages
The overhead caused by control messages relative to the total number of messages
shape is similar, the peaks are around 3.5% of the total bits
send in the network. As soon as the initialization phase is
over both ratios drop rapidly. The message ratio drops to
4% and the bit ratio becomes negligible at 0.3%. This is all
not taking possible enhancements into account. We are now
sending control messages even if nothing has changed. While
there is still room for improvement the overhead is negligible
if a maximization of sampling rates is possible.
VII. C ONCLUSION AND F UTURE W ORK
In this paper we have proposed SDF, an approach to maximizing the sampling rate in solar-harvesting sensor networks.
It supports the feasibility of solar-harvesting sensor networks
as a means to overcome energy constraints, which traditionally
have been posing a hard bound on sensor networks. We
introduced the notion of the energy neutral consumption rate,
at which the harvested and consumed energy are balanced, to
allow theoretically perpetual operation. We further discussed
the assumptions and theoretical models that constitute the
foundations for SDF. A simple cloud model, which models the
spatio-temporal distribution of solar radiation, was introduced
to establish a realistic evaluation environment.
SDF utilizes the harvested energy while remaining energy
neutral. It works in three simple steps that are repeated periodically on each node. First, a node approximates the energy
neutral consumption rate as the own consumption rate. Our
evaluation indicated that retaining no more than 30 samples is
sufficient for the prediction. Next, a node calculates a flow for
itself and the predecessors. This flow is bound by the minimum
of either its energy prediction or the possible throughput of
its successor nodes on the path to the data sink. During the
last step it sends control messages to all direct predecessors
bounding their allowed respective flow.
The model shows that updates, in a network with n nodes,
are propagated in log n steps in the expected, or a maximum
of n − 1 steps in the worst cases.
For realistic evaluation, we measured the impact of node and
cloud density on the sustained sampling rate, and hence the
performance of SDF, comparing it to the theoretical optimum,
as given in [1]. The results demonstrated that the minimal
sampling rate obtained by SDF is over 80% of the baseline’s
sampling rate. Comparing the predicted energy to the energy
neutral consumption rate illustrated a possible energy utilization of over 90%. Finally, they indicate that the message and
bit overhead is negligible compared to the increase in samples
retained. The control messages even under adverse situations
accounted for only 4% and 0.32% of the message and bit load
respectively.
We are currently deploying SDF on a solar harvesting sensor
network in Darmstadt to collect real world experience with
energy harvesting. In this course we are aiming at analysing
the underlying routing. Developing a solar-aware routing protocol that will complement SDF’s performance by giving a
balanced routing tree with short path lengths, while utilizing
available harvested energy, we are expecting to achieve even
higher sampling rates.
R EFERENCES
[1] A. Kansal, J. Hsu, S. Zahedi, and M. B. Srivastava, “Power Management in Energy Harvesting Sensor Networks,” ACM Transactions on
Embedded Computing Systems, 2007.
[2] V. Raghunathan, A. Kansal, J. Hsu, J. Friedman, and M. Srivastava,
“Design considerations for solar energy harvesting wireless embedded
systems,” in IPSN, 2005.
[3] X. Jiang, J. Polastre, and D. Culler, “Perpetual Environmentally Powered
Sensor Networks,” in IPSN, 2005.
[4] M. Minami, T. Morito, H. Morikawa, and T. Aoyama, “Solar Biscuit: a
battery-less wireless sensor network system for environmental monitoring applications,” in Workshop on Networked Sensing Systems, 2005.
[5] P. Sikka, P. Corke, and L. Overs, “Wireless sensor devices for animal
tracking and control,” in IEEE International Conference on Local
Computer Networks, 2004.
[6] C. Alippi, R. Camplani, C. Galperti, and M. Roveri, “A Robust,
Adaptive, Solar-Powered WSN Framework for Aquatic Environmental
Monitoring,” IEEE Sensors Journal, 2011.
[7] T. Clark, “Numerical Simulations with a Three-Dimensional Cloud
Model: Lateral Boundary Condition Experiments and Multicellular
Severe Storm Simulations.” Journal of Atmospheric Sciences, 1979.
[8] R. A. Anthes, “A Cumulus Parameterization Scheme Utilizing a OneDimensional Cloud Model,” Monthly Weather Review, 1977.
[9] S. Roundy, D. Steingart, L. Frechette, P. Wright, and J. Rabaey, “Power
sources for wireless sensor networks,” LNCS, 2004.
[10] C. Vigorito, D. Ganesan, and A. Barto, “Adaptive control of duty cycling
in energy-harvesting wireless sensor networks,” in IEEE Conference on
Sensor, Mesh and Ad Hoc Communications and Networks, 2007.
[11] A. Kansal and M. Srivastava, “An environmental energy harvesting
framework for sensor networks,” in Symposium on Low Power Electronics and Design, 2003.
[12] J. Hill, R. Szewczyk, A. Woo, S. Hollar, D. Culler, and K. Pister,
“System architecture directions for networked sensors,” ACM SIGPLAN
Notices, 2000.
[13] J. Polastre, R. Szewczyk, and D. Culler, “Telos: enabling ultra-low power
wireless research,” in IPSN, 2005.
[14] P. Corke, P. Valencia, P. Sikka, T. Wark, and L. Overs, “Long-Duration
Solar-Powered Wireless Sensor Networks,” in Workshop on Embedded
networked sensors, 2007.
[15] L. Lin, N. Shroff, and R. Srikant, “Asymptotically Optimal EnergyAware Routing for Multihop Wireless Networks With Renewable Energy
Sources,” IEEE/ACM Transactions on Networking, 2007.
[16] C. Intanagonwiwat, R. Govindan, D. Estrin, J. Heidemann, and F. Silva,
“Directed diffusion for wireless sensor networking,” IEEE/ACM Transactions on Networking, 2003.
[17] T. Voigt, H. Ritter, and J. Schiller, “Utilizing Solar Power in Wireless
Sensor Networks,” in IEEE International Conference on Local Computer
Networks, 2003.
[18] T. Voigt, H. Ritter, and J. Schiller, “Solar-aware routing in wireless
sensor networks,” Personal Wireless Communications, 2003.
[19] J. Schiller, A. Liers, H. Ritter, R. Winter, and T. Voigt, “ScatterWeb
- Low Power Sensor Nodes and Energy Aware Routing,” in Hawaii
International Conference on System Sciences, 2005.
[20] T. Voigt, A. Dunkels, J. Alonso, H. Ritter, and J. Schiller, “Solar-Aware
Clustering in Wireless Sensor Networks,” in International Symposium
on Computers and Communications, 2004.
[21] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “An
application-specific protocol architecture for wireless microsensor networks,” IEEE Transactions on Wireless Communications, 2002.
[22] W. Shu, X. Liu, Z. Gu, and S. Gopalakrishnan, “Optimal Sampling
Rate Assignment with Dynamic Route Selection for Real-Time Wireless
Sensor Networks,” in Real-Time Systems Symposium, 2008.
[23] S. Bandyopadhyay, Q. Tian, and E. Coyle, “Spatio-temporal sampling
rates and energy efficiency in wireless sensor networks,” IEEE/ACM
Transactions on Networking, 2005.
[24] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for
wireless networks,” in MobiCom, 2000.
[25] T. Brock, “Calculating solar radiation for ecological studies,” Ecological
Modelling, 1981.
[26] International earth rotation & reference systems service, “Useful Constants,” http://hpiers.obspm.fr/eop-pc/models/constants.html.
[27] Crossbow Technology Inc, “MICAz Datasheet,” www.openautomation.
net/uploadsproductos/micaz datasheet.pdf.
[28] A. Chipcon, “CC2420 datasheet,” http://focus.ti.com/lit/ds/symlink/
cc2420.pdf.
[29] O. Ghica, G. Trajcevski, P. Scheuermann, Z. Bischof, and N. Valtchanov,
“SIDnet-SWANS: A simulator and integrated development platform
for sensor networks applications,” in ACM Conference on Embedded
Network Sensor Systems, 2008.
[30] R. Barr and Z. Haas, “JiST/SWANS,” http://jist.ece.cornell.edu.